What do you call the material you use in the kitchen such as friedpan, pot, kettle etc.
What do you call the things you eat with such as plate, dish, fork, knife etc.
And what is the name generalizing both categories (friedpan, pot, fork knife)
Cutlery are the implements with which you eat; knife, fork, spoon.
Plates on which food is placed are called several things in Canada: dishes, china, tableware.
Items from which you drink are generally called glassware.
Items in which you cook are generally called pots and pans.
"Cutlery" is certainly correct to describe forks, knives and spoons, but in AmE we usually refer to it as "silverware" (whether or not it is made from genuine silver). So, for example, if you are seated at a restaurant table and your place setting has no eating implements, you would ask the server "May I have some silverware, please?"
in australia they say to
spoon, knife, fork = cutlery
plate, bowl, cup = crockery